Matt Cutts from Google has clarified the difference between old and new messages by saying that new messages also lack the yellow exclamation mark which is having in old messages.
Old Link Messages
In those cases, if you received the original link message, you have clear your link profile for low-quality links and submit the reconsider request. These messages will have a yellow sign of warning and they started from March.
New Link Messages
Not to worry much about these messages as these are sent for some of the links which are already distrusted by Google. However, Matt Cutts said if the rankings go down for some of the keywords, in those cases you should consider these messages as serious.
These messages will have more clear indications in the future and as per Google, they send 10 such messages per day to site owners.
If you have received any such message in recent times, you should download the backlinks profile from Webmaster tools sorted by date and should look for the link which was built recently.